Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		TaskB sol = new TaskB();
		sol.Solver();
		return;
	}
	public static class TaskB {
		public TaskB() {
			
		}
		double getArea(double h, double lb, double hb) {
			return lb * h + (hb - lb) * 0.5 * h;
		}
		public void Solver() {
			Scanner sc = new Scanner(System.in);
			int n = sc.nextInt();
			int h = sc.nextInt();
			double base = 0;
			double area = h * 0.5;
			double needArea = area / (double)n;
			double p = (1. / (double)h);
			double x0 = 0.0;
			for(int i = 0; i + 1 < n; ++i) {
				double lo = 0, hi = h - x0;
				for(int z = 0; z < 100; ++z) {
					double md = (lo + hi) * 0.5;
					if(getArea(md, base, base + p * md) < needArea) lo = md;
					else hi = md;
				}
				base += p * lo; 
				x0 += lo;
				System.out.println(x0);
			}
			sc.close();
		}
	}
}